A method and system for calculating stress-strain response of an engineered structure

Abstract

The application provides a method and system for calculating stress and strain response of engineering structure, and relates to the technical field of engineering structure analysis, wherein a few groups of material parameters are used to calculate stress and strain of engineering structure under complex temperature field through linear interpolation of material parameters to temperature; meanwhile, an error control strategy is combined in the explicit integration scheme, so that the constitutive model can simultaneously consider calculation speed, convergence and calculation error when used for stress and strain calculation of structure, the program does not need to divide a small increment step, the error control module is used to judge whether the error meets the requirements, if the error does not meet the requirements, the increment step is automatically reduced, and the calculation is restarted until the error meets the requirements, the error control module ensures the accuracy of the calculation program; the explicit integration scheme makes the structure of the calculation program simple, and iteration calculation is not needed, so that the calculation speed is ensured to be fast and the program convergence is strong, and the problem that convergence and calculation speed of nonlinear constitutive numerical calculation program are difficult to consider is overcome.

Description

Technical Field

[0001] This invention relates to the field of engineering structure analysis technology, and in particular to a method and system for calculating the stress-strain response of engineering structures. Background Technology

[0002] Constitutive theory is indispensable in structural strength design, deformation analysis, and stress-strain calculation, and has been widely applied in disciplines such as mechanical engineering, civil engineering, aerospace engineering, materials science, and nuclear power. Currently, the application of constitutive models in the local strength analysis of engineering structures is not yet mature, and its application in stress-strain calculation and deformation analysis of engineering structures still faces some challenges.

[0003] Constitutive models employ two integration schemes: explicit and implicit. Explicit integration schemes offer the advantages of fast computation and high convergence, as they require no iteration; however, they cannot guarantee computational accuracy and necessitate smaller time steps. Implicit integration schemes, on the other hand, achieve computational accuracy through numerical iteration and allow for larger time steps; however, numerical iteration incurs significant computational costs, resulting in slower computation and difficulty in guaranteeing convergence. In short, regardless of the integration scheme chosen, it is difficult to simultaneously balance computational speed, convergence, and error. This limitation restricts the application of advanced constitutive models in calculating local stress and strain and analyzing overall deformation in engineering structures. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for calculating the stress-strain response of engineering structures, which takes into account calculation speed, convergence and error.

[0005] To achieve the above objectives, the present invention provides the following solution:

[0006] A method for calculating the stress-strain response of an engineering structure, wherein the stress-strain response includes the stress tensor and strain tensor of the engineering structure; the method includes the following steps:

[0007] Determine the material parameters of the engineering structure at the current temperature.

[0008] The values ​​of each state variable of the engineering structure and the rate of change of each state variable are obtained; the state variables are used to characterize the deformation state or thermodynamic state of the engineering structure; the rate of change of the state variables is used to characterize the degree of change of the state variables over time.

[0009] For any given state variable, update the value of the state variable based on its value, its rate of change, and a preset time step.

[0010] Based on the material parameters and the values ​​of each state variable of the engineering structure at the current temperature, the stress tensor and strain tensor of the engineering structure are calculated.

[0011] The calculation error is determined based on the changes in the values ​​of each state variable and the material parameters of the engineering structure at the current temperature.

[0012] Determine whether the calculation error meets the preset precision; if not, adjust the preset time step and jump to the step "For any state variable, update the value of the state variable according to the value of the state variable, the rate of change of the state variable and the preset time step"; if yes, keep the preset time step unchanged.

[0013] Determine whether the engineering structure has yielded based on the yield function; if so, update the rate of change of each state variable based on the material parameters and values ​​of each state variable of the engineering structure at the current temperature; otherwise, keep the rate of change of each state variable unchanged.

[0014] Store the values ​​of each state variable and the rate of change of each state variable.

[0015] Jump to step "Determine the material parameters of the engineering structure at the current temperature" and perform stress-strain calculation for the next preset time step until the preset calculation time is reached.

[0016] Optionally, determining whether the calculation error meets the preset precision specifically includes:

[0017] Determine whether the calculation error is less than a preset error upper limit.

[0018] If so, then the calculation error is determined to meet the preset accuracy.

[0019] If not, then the calculation error is determined to not meet the preset accuracy.

[0020] Optionally, determining whether the calculation error meets the preset precision specifically includes:

[0021] Determine whether the calculation error is greater than a preset error upper limit.

[0022] If so, it is determined that the calculation error does not meet the preset precision, the preset time step is reduced, and the process jumps to the step "For any state variable, update the value of the state variable according to the value of the state variable, the rate of change of the state variable and the preset time step".

[0023] Otherwise, determine whether the calculation error is greater than a preset lower error limit.

[0024] If so, then the preset time step remains unchanged.

[0025] Otherwise, increase the preset time step.

[0026] Optionally, the state variables include: back stress tensor, isotropic hardening scalar, damage tensor, and inelastic strain tensor.

[0027] Optionally, determining whether the engineering structure has yielded based on the yield function specifically includes:

[0028] The equivalent stress is calculated based on the deviator of the stress tensor and the deviator of the back stress tensor.

[0029] The yield function value of the engineering structure is determined based on the equivalent stress, the isotropic hardening scalar, and the initial yield strength.

[0030] If the yield function value is greater than or equal to 0, the engineering structure is determined to have yielded; otherwise, the engineering structure is determined not to have yielded.

[0031] Optionally, updating the value of the state variable based on its value, the rate of change of the state variable, and a preset time step specifically includes:

[0032] The change in the state variable is determined based on the rate of change of the state variable and the preset time step.

[0033] The value of the state variable is updated based on its value and the amount of change.

[0034] Optionally, updating the rate of change of each state variable based on the material parameters and values ​​of each state variable of the engineering structure at the current temperature specifically includes:

[0035] For any given state variable, the values ​​of each state variable and the material parameters of the engineering structure at the current temperature are substituted into the rate of change update function of the state variable to update the rate of change of the state variable.

[0036] Optionally, the step of calculating the stress tensor and strain tensor of the engineering structure based on the material parameters and values ​​of various state variables at the current temperature specifically includes:

[0037] The strain tensor of the engineering structure is calculated based on the material parameters and the values ​​of each state variable of the engineering structure at the current temperature.

[0038] By substituting the material parameters of the engineering structure at the current temperature and the strain tensor into the stress-strain relationship, the stress tensor of the engineering structure is calculated.

[0039] Optionally, determining the material parameters of the engineering structure at the current temperature specifically includes:

[0040] Several actual sampling temperature points are determined; the current temperature is located between the minimum and maximum values ​​of the actual sampling temperature points.

[0041] Material parameters of the engineering structure were collected at each actual temperature point.

[0042] Based on the material parameters of the engineering structure collected at each actual temperature point, the material parameters of the engineering structure at the current temperature are determined.

[0043] Corresponding to the aforementioned method for calculating the stress-strain response of an engineering structure, the present invention also provides a system for calculating the stress-strain response of an engineering structure. When the system for calculating the stress-strain response of an engineering structure is run by a computer, it executes the method for calculating the stress-strain response of an engineering structure as described above.

[0044] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0045] This invention provides a method and system for calculating the stress-strain response of an engineering structure. The method includes: determining the material parameters of the engineering structure at a current temperature; acquiring the values ​​of each state variable of the engineering structure and the rate of change of each state variable; updating the value of any state variable based on its value, the rate of change of the state variable, and a preset time step; calculating the stress tensor and strain tensor of the engineering structure based on the material parameters of the engineering structure at the current temperature and the values ​​of each state variable; determining the calculation error based on the change in the values ​​of each state variable and the material parameters of the engineering structure at the current temperature; determining whether the calculation error meets a preset accuracy; if not, adjusting the preset time step and recalculating and updating the values ​​of the state variables; if yes, keeping the preset time step unchanged; determining whether the engineering structure has yielded based on the yield function; if yes, updating the rate of change of each state variable; otherwise, keeping the rate of change of each state variable unchanged; storing the values ​​of each state variable and the rate of change of each state variable; and jumping to the step "determining the material parameters of the engineering structure at the current temperature" to perform stress-strain calculation for the next preset time step until the preset calculation time is reached. This invention employs an explicit integration scheme, which has strong convergence, fast calculation speed, and simple program writing. Furthermore, it incorporates an error control strategy into the explicit integration scheme, which retains its characteristics of fast calculation speed and strong convergence while also ensuring a certain level of calculation accuracy. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 A flowchart of a method for calculating the stress-strain response of an engineering structure provided in Embodiment 1 of the present invention;

[0048] Figure 2 This is a flowchart of one embodiment of step S6 in the method provided in Embodiment 1 of the present invention;

[0049] Figure 3 A flowchart illustrating another implementation of step S6 in the method provided in Embodiment 1 of the present invention;

[0050] Figure 4 This is a schematic diagram of the theoretical framework of the viscoplastic constitutive model in the method provided in Embodiment 1 of the present invention;

[0051] Figure 5 This is a schematic diagram of the equivalent stress calculation results of the turbine blades before and after creep in the method provided in Embodiment 1 of the present invention;

[0052] Figure 6 This is a schematic diagram of the calculation results of the equivalent inelastic strain of the turbine blade after 100 hours of creep in the method provided in Embodiment 1 of the present invention;

[0053] Figure 7 This is a schematic diagram of a system for calculating the stress-strain response of an engineering structure, provided in Embodiment 2 of the present invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] Constitutive theory is indispensable in structural strength design, deformation analysis, and stress-strain calculation, and has been widely applied in disciplines such as mechanical engineering, civil engineering, aerospace engineering, materials science, and nuclear power.

[0056] Aerospace hot-end components operate under high-temperature and complex loads, with localized multiaxial stress states. These loads change continuously over time, and service durations can reach thousands of hours. Accurate calculation of local stress-strain fields and overall structural deformation requires the development of advanced constitutive theories. Precise stress-strain calculations and deformation analyses are fundamental to structural design, strength evaluation, and life prediction.

[0057] For aerospace component structures, designers are required not only to minimize component mass, but also to ensure sufficient strength reserves and high reliability. The detailed design of any structure needs to be accurately grasped. Traditional structural design and analysis methods based on linear elasticity or classical elastoplastic theory usually have large safety margins and are difficult to apply to complex structures. With the development of technology, they have shown obvious shortcomings. It is necessary to continuously develop advanced constitutive theories for stress-strain calculation and deformation analysis of engineering structures.

[0058] Accurate prediction of structural deformation requires the support of advanced material constitutive models. Accurate deformation analysis can improve the working efficiency of engineering structures and reduce their failure probability. NASA research shows that for aero engines, reducing the turbine clearance by 0.254 mm can reduce fuel consumption by 1% while achieving the same power output. The turbine inlet temperature can also be reduced by 10°C. Based on the current situation, this could save $1.6 billion in fuel costs in 2002 alone.

[0059] It is evident that advanced life management technology requires constitutive models to provide accurate local stress and strain states of the structure. Advanced constitutive models help extend overhaul intervals and maintenance cycles, extend the service life of components, and reduce the maintenance costs of engineering structures. Related studies show that if advanced life management technology had been used since 1988, approximately $3.5 billion in maintenance costs could have been saved by 2000.

[0060] Currently, the application of advanced constitutive theory in the local strength analysis of engineering structures is not yet mature. Its application in stress-strain calculation and deformation analysis of engineering structures still faces some problems that have not been well resolved. Among these problems, the "balance between calculation speed, convergence, and accuracy" and the "temperature dependence of material parameters" are particularly prominent. Inelastic stress-strain analysis is a nonlinear analysis, and it is usually difficult to balance calculation speed, convergence, and accuracy. Generally, calculation programs with strong convergence require very small increment step sizes, which greatly increases the calculation cost and requires a lot of time to complete the structural strength calculation and verification. On the other hand, setting large increment step sizes usually leads to the program failing to converge, causing the calculation to terminate and making it impossible to complete the strength analysis, and the calculation accuracy is difficult to guarantee.

[0061] The purpose of this invention is to provide a method and system for calculating the stress-strain response of engineering structures, which takes into account calculation speed, convergence and error.

[0062] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0063] Example 1:

[0064] This embodiment provides a method for calculating the stress-strain response of an engineering structure. The calculation of the stress-strain response specifically includes the calculation of the stress tensor and the strain tensor, such as... Figure 1 As shown, the method includes the following steps:

[0065] S1. Determine the material parameters of the engineering structure at the current temperature.

[0066] S2. Obtain the values ​​of each state variable of the engineering structure and the rate of change of each state variable; the state variables are used to characterize the deformation state or thermodynamic state of the engineering structure; the rate of change of the state variables is used to characterize the degree of change of the state variables over time.

[0067] S3. For any state variable, update the value of the state variable based on its value, its rate of change, and a preset time step. In this embodiment, an explicit integration scheme is preferably used to update the state variable.

[0068] S4. Based on the material parameters and values ​​of each state variable of the engineering structure at the current temperature, calculate the stress tensor and strain tensor of the engineering structure. At this point, the stress tensor and strain tensor of all points of the engineering structure at the current temperature and at the end of the current time step have been calculated. To calculate the stress and strain at the next time step, it is necessary to determine the rate of change of each state variable at the beginning of the next time step.

[0069] S5. Determine the calculation error based on the changes in the values ​​of each state variable and the material parameters of the engineering structure at the current temperature.

[0070] S6. Determine whether the calculation error meets the preset precision; if not, execute step S7 to adjust the preset time step and jump to step S3 "For any state variable, update the value of the state variable according to the value of the state variable, the rate of change of the state variable and the preset time step"; if yes, keep the preset time step unchanged and directly execute step S8.

[0071] S8. Determine whether the engineering structure has yielded based on the yield function; if so, proceed to step S9, update the rate of change of each state variable based on the material parameters and values ​​of each state variable at the current temperature, and proceed to step S10; otherwise, keep the rate of change of each state variable unchanged and directly proceed to step S10. Step S9 specifically includes:

[0072] For any state variable, the material parameters of the engineering structure at the current temperature and the values ​​of each state variable are substituted into the rate of change update function of the state variable to update the rate of change of the state variable.

[0073] S10. Store the values ​​of each state variable and the rate of change of each state variable. Then jump to the step "Determine the material parameters of the engineering structure at the current temperature" to perform stress and strain calculations for the next preset time step until the preset calculation time is reached. Through the above steps, stress and strain calculations of the engineering structure under complex temperature fields can be realized over a continuous calculation time.

[0074] As an optional implementation method, such as Figure 2 The flowchart shown includes step S6, which determines whether the calculation error meets the preset precision. Specifically, this includes:

[0075] S61. Determine whether the calculation error is less than the preset error upper limit.

[0076] If so, then execute S62 to determine that the calculation error meets the preset accuracy.

[0077] If not, then execute S63 to determine that the calculation error does not meet the preset accuracy.

[0078] As another alternative implementation method, such as Figure 3 The flowchart shown, step S6, determining whether the calculation error meets the preset precision, may further include:

[0079] S61. Determine whether the calculation error is greater than the preset error upper limit.

[0080] If so, proceed to step S62 to determine that the calculation error does not meet the preset precision, reduce the preset time step, and jump to step S3 "For any state variable, update the value of the state variable according to the value of the state variable, the rate of change of the state variable and the preset time step".

[0081] Otherwise, proceed to step S63 to determine whether the calculation error is greater than the preset lower limit of error.

[0082] If so, then execute step S64 to keep the preset time step unchanged.

[0083] Otherwise, proceed to step S65 to increase the preset time step.

[0084] In some implementations, the state variables may include: back stress tensor, isotropic hardening scalar, damage tensor, and inelastic strain tensor.

[0085] After determining in step S6 that the calculation error meets the preset accuracy requirement, it is necessary to determine whether the material of the engineering structure has yielded. If the material has yielded, the rate of change of the state changes at the end of the incremental step, and the rate of change of the state variable needs to be calculated and updated; if the material has not yielded, no calculation update is required. Step S8 determines whether the engineering structure has yielded based on the yield function, specifically including:

[0086] S81. The equivalent stress is calculated based on the deviator of the stress tensor and the deviator of the back stress tensor.

[0087] S82. Determine the yield function value of the engineering structure based on the equivalent stress, the isotropic hardening scalar, and the initial yield strength.

[0088] S83. If the yield function value is greater than or equal to 0, it is determined that the engineering structure has yielded; otherwise, it is determined that the engineering structure has not yielded.

[0089] Step S3 updates the value of the state variable based on the value of the state variable, the rate of change of the state variable, and the preset time step, specifically including:

[0090] S31. Determine the change amount of the state variable based on the rate of change of the state variable and the preset time step.

[0091] S32. Update the value of the state variable based on the value of the state variable and the amount of change of the state variable.

[0092] Step S4 calculates the stress tensor and strain tensor of the engineering structure based on the material parameters and values ​​of each state variable at the current temperature, specifically including:

[0093] S41. Based on the material parameters and the values ​​of each state variable of the engineering structure at the current temperature, the strain tensor of the engineering structure is calculated.

[0094] S42. Substitute the material parameters of the engineering structure at the current temperature and the strain tensor into the stress-strain relationship to calculate the stress tensor of the engineering structure.

[0095] Step S1 determines the material parameters of the engineering structure at the current temperature, specifically including:

[0096] S11. Determine several actual sampling temperature points; the current temperature is located between the minimum and maximum values ​​of the actual sampling temperature points.

[0097] S12. At each actual sampling temperature point, collect the material parameters of the engineering structure.

[0098] S13. Based on the material parameters of the engineering structure collected at each actual temperature point, determine the material parameters of the engineering structure at the current temperature.

[0099] The following example illustrates the method for calculating the stress-strain response of engineering structures provided in this embodiment. Typical constitutive models available include elastoplastic, viscoplastic, and crystalline plastic constitutive models. While the elastoplastic model is relatively simple and cannot describe the time-dependent creep process of high-temperature structural materials, the crystalline plastic model is too complex and not easily understood. The viscoplastic model, however, can describe the time-dependent creep process and is of moderate difficulty, allowing for relatively accurate simulation of the local stress-strain response of hot-end components. Furthermore, the viscoplastic model can simultaneously calculate time-dependent creep deformation and time-independent plastic deformation, and has been widely used in engineering.

[0100] This example uses an aero-engine turbine blade as a specific case to fully introduce the numerical implementation method of the viscoplastic constitutive model in actual engineering structures. The method for calculating the stress-strain response of the engineering structure in this example mainly includes the following steps:

[0101] 1.1 Material parameters are interpolated for temperature.

[0102] Explicit integration schemes balance program speed and computational accuracy. However, to calculate the mechanical response of turbine blades under complex temperature fields, relying solely on a few sets of material parameters at specific temperatures is far from sufficient. Currently, there is no mature and unified method in the engineering field for solving the problem of "how to calculate the mechanical response of engineering structures under complex temperature fields using limited material parameters." Therefore, in this example, it is necessary to interpolate the material parameters with respect to temperature. The purpose of interpolating the material parameters with respect to temperature is to obtain the material parameters at any temperature within a certain temperature range.

[0103] Read the temperature T at the calculation point, determine the temperature range within which the calculation point temperature falls, and perform interpolation based on the two endpoints of the temperature range. If T∈[T1,T2), the material parameters at temperature T1 can be denoted as... The material parameters at temperature T2 can be denoted as: The material parameters at temperature T can be expressed as:

[0104]

[0105] Thus, the material parameters at temperature T are obtained. If the temperature of the calculation point exceeds the highest temperature, the material parameters of the highest temperature are assigned to that point. If the temperature of the calculation point is lower than the lowest temperature, the material parameters of the lowest temperature are assigned to that point. The material parameters are interpolated only and not extrapolated. Then, the material parameters are used as input to the viscoplastic constitutive model to calculate the mechanical response of the structural material.

[0106] 1.2 Read the initial values ​​of the state variables and their rates of change.

[0107] Material parameters are used as input to the viscoplastic constitutive model. The aforementioned material parameters are input into the viscoplastic constitutive model to calculate the stress-strain response of the engineering structural material. Stress, strain, and state variables are the output variables of the viscoplastic constitutive model. During the calculation process, the viscoplastic constitutive model can output some state variables of interest to the user. These state variables can be used to visualize the inelastic strain and damage of the engineering structure. Therefore, they need to be calculated and updated in the program. Before calculating the values ​​of the state variables, their initial values ​​and rates of change need to be read. The basic theoretical framework of the existing viscoplastic constitutive model is as follows: Figure 4 As shown:

[0108] The stress-strain relationship expression defines the relationship between the stress tensor and the strain tensor, where σ ij Denotes the stress tensor, δ ij Let be a Kronecker tensor, where the subscripts ij denote rows and columns in the two-dimensional matrix (i = 1–3, j = 1–3), and the subscript kk denotes dummy indices (k = 1–3). Here, the "index notation" is used, following Einstein's summation convention. λ is the Lamé constant, which can be expressed as λ = E / (1+μ) / (1-2μ), where E is the elastic modulus, μ is Poisson's ratio, G is the shear modulus, and ε... ij Represents the strain tensor. It represents the inelastic strain tensor.

[0109] The equivalent stress expression treats the stress tensor as a scalar, where σ eq σ represents the equivalent stress. ij ' represents the deviator of the stress tensor, X represents the back stress, X ij 'Indicates the deviance of the back stress tensor.

[0110] The equivalent inelastic strain rate expression treats the inelastic strain rate tensor as a scalar, where... This represents the rate of change of the equivalent inelastic strain. It represents the rate of change of the inelastic strain tensor.

[0111] The flow equation defines the expression for the rate of change of the inelastic strain tensor. The flow equation includes the yield function, back stress, isotropic hardening scalar, and damage, where f is the yield function, K is the material parameter (drag stress), and n is the flow equation exponent. This indicates the deviance of the stress tensor after damage. This represents the equivalent stress after considering damage, where D represents damage.

[0112] The yield function is defined by its expression, where R represents the isotropic hardening scalar and k0 represents the initial yield strength.

[0113] The back stress equation defines the expression for the rate of change of back stress, where, Let Jx represent the rate of change of the back stress tensor, c be the parameter of the linear hardening term, a be the parameter of the dynamic hardening term, β be the parameter of the thermal recovery term, r be the exponent of the thermal recovery term, and J2(X) represent the second invariant of the back stress.

[0114] The isotropic hardening scalar equation defines the expression for the rate of change of the isotropic hardening scalar, where b is the isotropic scalar rate control parameter and W is the isotropic scalar saturation value.

[0115] The damage equations define expressions for the rate of change of damage, where... K represents the second invariant of effective stress after damage has been considered. d n is the damage drag stress parameter. d k is the damage stress index. d This is the damage rate control parameter.

[0116] Conventional viscoplastic theory typically uses three internal variables: back stress, isotropic hardening scalar, and damage. In this example, the constitutive calculation program uses four state variables: back stress, isotropic hardening scalar, damage, and inelastic strain. Back stress primarily describes the kinematic hardening mechanics of the blade material; the isotropic hardening scalar describes the isotropic hardening mechanics of the blade material; damage describes the accelerated creep phenomenon in the third stage of blade material creep; and inelastic strain describes the irreversible deformation of the blade material. The four state variables are used to record the magnitudes of the back stress, isotropic hardening scalar, damage, and inelastic strain of the blade material.

[0117] In this step, the back stress, isotropic hardening scalar, damage, and inelastic strain state variables and their rates of change are read at the end of the previous increment step (at the beginning of this increment step). If this increment step is the initial increment step, the values ​​of the state variables here are set to 0.

[0118] 1.3 Update the state variable values.

[0119] Substituting the read state variables and their rates of change into the viscoplastic constitutive model, the calculation and update of the state variables can be performed. Based on the state variables and their rates of change at the beginning of this increment step, using an explicit integration scheme (here, the Voigt notation method is employed), the state variables at the end of this increment step are calculated. There are four sets of state variables. Knowing their values ​​and rates of change at time t, the state variable values ​​at time t+Δt can be expressed as:

[0120] Back stress: Where X represents the back stress and i represents the back stress component.

[0121] Isotropic hardening scalar: Where R represents the isotropic hardening scalar.

[0122] damage: Where D represents damage.

[0123] Inelastic strain: Where ε in Let represent the inelastic strain in the flow equation, and let i represent the inelastic strain component.

[0124] 1.4 Assemble the stiffness matrix and update the stress and strain.

[0125] After updating the state variables, the stress and strain also need to be updated to complete the calculation. Stress and strain are not state variables; their calculation requires iterative calculation based on the stiffness matrix. The stiffness matrix is ​​assembled from the elastic constants (material parameters E, μ, G) at temperature T, based on the elastic modulus E, Poisson's ratio μ, and shear modulus G, and used for iterative solving in the finite element software. Here, E, μ, and G are some material parameters of the viscoplastic constitutive model. The stiffness matrix of an isotropic material can be expressed as:

[0126]

[0127] Here, we take the cast high-temperature alloy K417G as an example. K417G is the material used to manufacture blades. It is an isotropic material with only two independent elastic constants: the elastic modulus E and the Poisson's ratio μ.

[0128] G is the shear modulus. There is a conversion relationship between the shear modulus and the elastic modulus of isotropic materials, as shown in the following formula:

[0129]

[0130] Stress and strain are updated according to the following formula. Here, the "index notation method" is used. The subscript ij represents the row and column in the two-dimensional matrix (i = 1 to 3, j = 1 to 3), and the subscript kk is the dummy index (k = 1 to 3), following the Einstein summation convention.

[0131]

[0132] 1.5 Error control strategy to determine whether the calculation error meets the requirements.

[0133] After completing the state variable and stress-strain calculations and updates, it is necessary to determine the calculation error. If the error meets the requirements, the calculation for the next increment step can begin; otherwise, recalculation is required. Since an explicit integration scheme is used, an error control strategy is necessary to ensure calculation accuracy. In each time increment step, the calculation error can be defined as:

[0134]

[0135] Where Δ represents the change, Δε in This represents the change in inelastic strain, mainly used to describe inelastic deformation. E represents the elastic modulus, and ΔJ² represents the second invariant of the stress tensor, which can be expressed as:

[0136] Where S ij It represents the deviance of the stress tensor.

[0137] The stress tensor can be expressed as:

[0138]

[0139] The deviance of the stress tensor can be expressed as:

[0140]

[0141] By manually setting the upper and lower limits of the error, the time increment step of the explicit integration scheme can be controlled.

[0142] The upper and lower limits of error set by the user are denoted as error. low With error up The upper and lower limits of error are recommended to be determined according to the following formulas:

[0143] error low =1.0×10 -5

[0144] error up =1.0×10 -4

[0145] If the error is less than the lower limit, the calculation result of this step is retained, and the time step size of the next incremental step is increased to twice the original step size.

[0146] If the error is greater than the lower limit but less than the upper limit, the calculation result of this step is retained, and the time step size of the next incremental step remains unchanged.

[0147] If the error exceeds the upper limit, it indicates that the error is too large. In this case, the calculation result of this step is invalidated, the time step size of this step is reduced, the time step size of this incremental step is set to 0.5 times the original step size, and the calculation is performed again.

[0148] 1.6 Determine whether yielding has occurred.

[0149] If the error meets the requirements, it is necessary to determine whether the material has yielded. If the material has yielded, the rate of change of state changes at the end of the increment step changes, requiring a calculation update; if the material has not yielded, no calculation update is needed. First, it is necessary to determine whether the material has yielded, based on the state variables at the end of the increment step. The yield function f can be expressed as:

[0150]

[0151] Where R is the isotropic hardening scalar, k0 is the initial yield strength, and the equivalent stress can be written as:

[0152]

[0153] To determine whether the material has yielded, the yield function f is greater than or equal to 0, indicating that the material has yielded; otherwise, it indicates that the material has not yielded. If the material has yielded, the rate of change of the state variable needs to be updated and stored for the next increment step. If the material has not yielded, there is no need to update the rate of change of the state variable, saving computational costs.

[0154] 1.7 Calculate the rate of change of the updated state variables.

[0155] If the previous step determined that the material had yielded, then based on the inelastic strain, back stress, isotropic hardening scalar, and damage at the end of the increment step (t+Δt), calculate the inelastic strain rate, back stress rate, isotropic hardening scalar rate, and damage rate at the end of the increment step, and store the state variables. If the previous step determined that the material had not yielded, then end the calculation of this increment step and directly proceed to the calculation of the next increment step.

[0156] 1.8 Store state variables and their rates of change.

[0157] The inelastic strain, back stress, isotropic hardening scalar, and rate of change of damage state at the end of the increment step are stored as the inelastic strain, back stress, isotropic hardening scalar, and rate of change of damage state at the beginning of the next increment step, and are then called upon for the calculation in the next increment step.

[0158] 1.9 The constitutive model was written into a calculation program, and the numerical implementation of the constitutive model was completed.

[0159] In this example, the stress-strain response of the engineering structure material at any temperature and within one increment step is completed through the steps 1.1 to 1.8 above. However, in practical applications, it is often necessary to calculate the stress-strain response under complex temperature fields with long duration. Therefore, by using commercial finite element software in combination with constitutive programs and with the help of the finite element software platform, the stress-strain calculation of the engineering structure under complex temperature fields with long duration can be completed.

[0160] This example uses the general-purpose commercial software ABAQUS to calculate the mechanical response of a turbine blade. The constitutive model can be written into a calculation program using the method described above. Combined with finite element software and constitutive calculation subroutines, the strength calculation of the turbine blade can be performed. The calculation results can be referenced. Figures 5-6 ,in Figure 5 This represents the equivalent stress distribution before and after creep. Figure 6 This represents the equivalent inelastic strain after 100 hours of creep.

[0161] Based on the above, the method for calculating the stress-strain response of engineering structures provided in this embodiment has the following advantages: Linear interpolation of material parameters with respect to temperature allows for the calculation of stress and strain in engineering structures under complex temperature fields using several sets of material parameters; advanced constitutive theory can be applied more scientifically and conveniently to calculate the mechanical response of engineering structures; the explicit integration scheme ensures strong convergence, fast calculation speed, and simple program writing; and an error control strategy is incorporated into the explicit integration scheme to ensure that the constitutive model, when used for structural stress-strain calculation, possesses both fast calculation speed and high convergence while maintaining a certain level of calculation error. It can simultaneously consider the calculation speed, convergence, and calculation error of the program. The program does not require dividing into extremely small increment steps; the error control module determines whether the error meets the requirements. If the error does not meet the requirements, the increment step size is automatically reduced, and the calculation restarts until the error meets the requirements. The error control module ensures the accuracy of the calculation program; the explicit integration scheme simplifies the calculation program structure, eliminates the need for iterative calculations, and ensures fast calculation speed and strong program convergence.

[0162] Example 2:

[0163] Furthermore, the method of Embodiment 1 of the present invention can also be used by means of Figure 7 The system architecture shown is used to calculate the stress-strain response of an engineering structure. For example... Figure 7 As shown, the system for calculating the stress-strain response of an engineering structure may include a material parameter determination module, a data reading module, a state variable update module, a stress-strain calculation module, a calculation error determination module, a calculation accuracy judgment module, a yield strength judgment module, a rate of change update module, and a data storage module; some modules may also have sub-units to implement their functions, for example, the stress-strain calculation module may also include a stress tensor calculation unit and a strain tensor calculation unit. Of course, Figure 7 The architecture shown is merely exemplary; it can be omitted as needed when implementing different functionalities. Figure 7 One or at least two components of the system shown.

[0164] The program portion of a technology can be considered a "product" or "artifact" existing in the form of executable code and / or related data, and is involved in or implemented through a computer-readable medium. Tangible, permanent storage media can include memory or storage used by any computer, processor, or similar device or related module. For example, various semiconductor memories, tape drives, disk drives, or any similar device capable of providing storage functionality for software.

[0165] All software, or parts thereof, may sometimes communicate via networks, such as the Internet or other communication networks. Such communication can load software from one computer device or processor to another. For example, loading software from a server or host computer of a video object detection device to a hardware platform of a computer environment, or another computer environment that implements the system, or a system with similar functionality related to providing the information needed for object detection. Therefore, another medium capable of transmitting software elements can also be used as a physical connection between local devices, such as light waves, radio waves, electromagnetic waves, etc., propagated through cables, fiber optic cables, or air. Physical media used for carrier waves, such as cables, wireless connections, or fiber optic cables, can also be considered as media carrying software. In this context, unless limited to tangible "storage" media, the term "readable medium" for a computer or machine refers to the medium involved in the execution of any instructions by the processor.

[0166] Specific examples are used in this article, but the above description is only to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only for the purpose of helping to understand the method and core ideas of the present invention. Those skilled in the art should understand that the various modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, and thus, they can be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.

[0167] Furthermore, those skilled in the art will recognize that, based on the principles of this invention, there will be variations in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as limiting the invention.

Claims

1. A method for calculating the stress-strain response of an engineering structure, wherein the stress-strain response includes a stress tensor and a strain tensor; characterized in that, The method includes the following steps: Determine the material parameters of the engineering structure at the current temperature; The values ​​of each state variable and the rate of change of each state variable of the engineering structure are obtained; the state variables are used to characterize the deformation state or thermodynamic state of the engineering structure, and the state variables include the back stress tensor, the isotropic hardening scalar, the damage tensor, and the inelastic strain tensor; the rate of change of the state variables is used to characterize the degree of change of the state variables over time. For any state variable, an explicit integration scheme is adopted to update the value of the state variable based on the value of the state variable, the rate of change of the state variable, and a preset time step. Based on the material parameters and values ​​of various state variables of the engineering structure at the current temperature, the stress tensor and strain tensor of the engineering structure are calculated. The calculation error is determined based on the changes in the values ​​of each state variable and the material parameters of the engineering structure at the current temperature; Determine whether the calculation error meets the preset precision; if not, adjust the preset time step and jump to step "For any state variable, adopt an explicit integration scheme to update the value of the state variable according to the value of the state variable, the rate of change of the state variable and the preset time step"; if yes, keep the preset time step unchanged. Determine whether the engineering structure has yielded based on the yield function; if so, update the rate of change of each state variable based on the material parameters and values ​​of each state variable of the engineering structure at the current temperature; otherwise, keep the rate of change of each state variable unchanged. Store the values ​​of each state variable and the rate of change of each state variable; Jump to step "Determine the material parameters of the engineering structure at the current temperature", and perform stress and strain calculations for the next preset time step until the preset calculation time is reached; Determining the material parameters of the engineering structure at the current temperature specifically includes: Several actual sampling temperature points are determined, and the current temperature is located between the minimum and maximum values ​​of the actual sampling temperature points; At each actual temperature point, the material parameters of the engineering structure were collected; Based on the material parameters of the engineering structure collected at each actual temperature point, the material parameters of the engineering structure at the current temperature are determined by linear interpolation. For any given state variable, an explicit integration scheme is employed to update the value of the state variable based on its value, its rate of change, and a preset time step. Specifically, this includes: The change in the state variable is determined based on the rate of change of the state variable and the preset time step. The value of the state variable is updated based on its value and the amount of change. Determining whether the engineering structure has yielded based on the yield function specifically includes: The equivalent stress is calculated based on the deviator of the stress tensor and the deviator of the back stress tensor. The yield function value of the engineering structure is determined based on the equivalent stress, the isotropic hardening scalar, and the initial yield strength. If the yield function value is greater than or equal to 0, the engineering structure is determined to have yielded; otherwise, the engineering structure is determined not to have yielded.

2. The method for calculating the stress-strain response of an engineering structure according to claim 1, characterized in that, The determination of whether the calculation error meets the preset precision specifically includes: Determine whether the calculation error is less than a preset error upper limit; If so, then the calculation error is determined to meet the preset precision. If not, then the calculation error is determined to not meet the preset accuracy.

3. The method for calculating the stress-strain response of an engineering structure according to claim 1, characterized in that, The determination of whether the calculation error meets the preset precision specifically includes: Determine whether the calculation error is greater than a preset error upper limit; If so, it is determined that the calculation error does not meet the preset precision, the preset time step is reduced, and the process jumps to the step "For any state variable, adopt an explicit integration scheme to update the value of the state variable according to the value of the state variable, the rate of change of the state variable and the preset time step". Otherwise, determine whether the calculation error is greater than a preset lower limit of error; If so, then the preset time step remains unchanged; Otherwise, increase the preset time step.

4. The method for calculating the stress-strain response of an engineering structure according to claim 1, characterized in that, The step of updating the rate of change of each state variable based on the material parameters and values ​​of each state variable of the engineering structure at the current temperature specifically includes: For any given state variable, the values ​​of each state variable and the material parameters of the engineering structure at the current temperature are substituted into the rate of change update function of the state variable to update the rate of change of the state variable.

5. The method for calculating the stress-strain response of an engineering structure according to claim 1, characterized in that, The calculation of the stress tensor and strain tensor of the engineering structure based on the material parameters and values ​​of various state variables at the current temperature specifically includes: The strain tensor of the engineering structure is calculated based on the material parameters and the values ​​of each state variable of the engineering structure at the current temperature. By substituting the material parameters of the engineering structure at the current temperature and the strain tensor into the stress-strain relationship, the stress tensor of the engineering structure is calculated.

6. A system for calculating the stress-strain response of an engineering structure, characterized in that, When the system for calculating the stress-strain response of an engineering structure is run by a computer, it performs the method for calculating the stress-strain response of an engineering structure as described in any one of claims 1-5.

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